Schaum's Outline of Theory and Problems of Advanced Calculus, Issue 2
-- First edition (1968) sold more than 347,000 copies and was translated into nine languages-- Advanced calculus is a required course for over 163,000 students, including all math majors and many science and engineering majors-- Important new chapters, on Topology and LaPlace Transforms enhance the book's cross-disciplinary usage-- Contains essential new theorems with explanatory proofs
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absolutely convergent assume axis called Cauchy's Chapter complex numbers conditional convergence constant continued fraction conv corresponding countable curvilinear coordinates defined DEFINITE INTEGRALS denoted differential diverges dx converges dx dx dx dy elliptic integral equation Evaluate example exists Fourier series function geometrically graph Green's theorem Hence Hint IMPROPER INTEGRALS infinite series integral becomes integral converges integrand Jacobian L'Hospital's rule Let f(x lim f(x line integral mean value theorem Method MISCELLANEOUS PROBLEMS monotonic increasing obtain Parseval's identity partial derivatives pole positive integer positive number power series Prob Problem 13 Prove that f Prove that lim radius rational number real numbers region bounded required result follows sequence series converges simple closed curve sin2 single-valued surface tangent line Taylor's theorem Test for convergence transformation uniformly convergent variable vector xy plane